SKUTTERUDITES: A Phonon-Glass-Electron Crystal Approach to Advanced Thermoelectric Energy Conversion Applications

Transcription

1 Annu. Rev. Mater. Sci : Copyright c 1999 by Annual Reviews. All rights reserved SKUTTERUDITES: A Phonon-Glass-Electron Crystal Approach to Advanced Thermoelectric Energy Conversion Applications G. S. Nolas Research and Development Division, Marlow Industries Inc., Dallas, Texas D. T. Morelli General Motors Research and Development Center, Warren, Michigan Terry M. Tritt Department of Physics and Astronomy, Kinard Laboratory, Clemson University, Clemson, South Carolina KEY WORDS: electronic refrigeration, thermopower, semiconductors ABSTRACT Recently there has been a resurgence of research efforts related to the investigation of new and novel materials for small-scale thermoelectric refrigeration and power generation applications. These materials need to couple and optimize a variety of properties in order to exhibit the necessary figure of merit, i.e. the numerical expression that is commonly used to compare one potential thermoelectric material with another. The figure of merit is related to the coefficient of performance or efficiency of a particular device made from a material. The best thermoelectric material should possess thermal properties similar to that of a glass and electrical properties similar to that of a perfect singlecrystal material, i.e. a poor thermal conductor and a good electrical conductor. Skutterudites are materials that appear to have the potential to fulfill such criteria. These materials exhibit many types of interesting properties. For example, skutterudites are members of a family of compounds we call open structure or cage-like, materials. When atoms are placed into the interstitial voids or cages of these materials, the lattice thermal conductivity can be substantially reduced /99/ $

2 90 NOLAS, MORELLI & TRITT compared with that of unfilled skutterudites. These compounds exhibit electrical properties ranging from that of low-temperature superconductors to narrow gap semiconductors. INTRODUCTION TO THERMOELECTRIC PHENOMENA AND APPLICATIONS Background A discussion of thermoelectric effects should start with the most fundamental thermoelectric phenomenon, the Seebeck effect. In the early 1800s, Seebeck observed that if two dissimilar materials are joined together and the junctions are held at different temperatures (T and T + T) a voltage difference ( V) is developed that is proportional to the temperature difference. The ratio of the voltage developed to the temperature gradient ( V/ T) is related to an intrinsic property of the materials called the Seebeck coefficient (α) or thermopower. The Seebeck coefficient is very low for metals (of the order of 1 to 10 µv/k) and much larger for semiconductors (10 2 to 10 3 µv/k). A related effect was discovered a few years later by Peltier, who observed that if a current is passed through the junction of two dissimilar materials, heat is reversibly absorbed or rejected at the junction depending on the current direction. This phenomenon, called the Peltier effect, is the basis for many modern day thermoelectric cooling devices. These two phenomena are illustrated in Figure 1a and b. The relationship between these two effects is given by the Peltier coefficient, π = αt. 1. The rate at which the heat is reversibly liberated or rejected at the junction ( Q P = dq P /dt)isgivenby Q P =αit, 2. where I is the current through the junction and T is the temperature in Kelvin. The versatility of applications utilizing thermoelectric materials is illustrated in Figure 2, which shows a diagram of a thermoelectric module composed of an n-type (negative thermopower and electron carriers) and a p-type (positive thermopower and hole carriers) semiconductor material connected through metallic electrical contact pads. Thermoelectric energy conversion can be obtained when a temperature difference is externally imposed. Thermoelectric cooling devices utilize the Peltier heat generated when an electric current is passed through a thermoelectric material to provide a temperature gradient with heat

3 SKUTTERUDITES 91 Figure 1 Illustration of the thermoelectric phenomena: (left) Seebeck effect, (right) Peltier effect. Figure 2 A thermoelectric module illustrating the versatility of these materials for use in solidstate thermoelectric refrigeration or in power generation. The thermoelectric module is composed of an n-type and a p-type semiconducting material connected electrically in series through metallic electrical contact pads and thermally in parallel between ceramic ends.

4 92 NOLAS, MORELLI & TRITT being absorbed on the cold side, transferred through or pumped by the charge carriers in the thermoelectric materials, and rejected at the heat sink, thus providing a refrigeration capability. The advantages of solid-state thermoelectric devices are compactness, quietness (no moving parts), and localized heating or cooling. Some applications include cooling or temperature stabilization of CCDs, infrared detectors, laser diodes, low-noise amplifiers, and computer chips. Common applications include reversible heating/cooling of picnic coolers. Given the harmful effect of standard CFC and greenhouse refrigeration gases on the environment, as well as the need for small-scale localized cooling in computers and electronics, the field of thermoelectrics is in need of higher performance materials than those that currently exist. In addition, as the future field of cryoelectronics (possibly utilizing high-t c superconducting electronics) develops, the need for lower temperature ( K) and higher performance thermoelectric materials becomes more prevalent. Thermoelectric materials are also being considered in the automobile industry for use in the next generation vehicle. These uses range from power generation utilizing waste engine heat through the exhaust and radiator cooling system, to seat coolers for comfort, or electronic component cooling. The potential of a material for thermoelectric applications is determined by the material s figure of merit, Z = α2 σ λ, 3. where α is the Seebeck coefficient, σ the electrical conductivity, and λ the total thermal conductivity (λ = λ L,λ E ; the lattice and electronic contributions, respectively). Because the dimensions of Z are inverse temperature, a more convenient quantity is the dimensionless figure of merit ZT, where T is absolute temperature. The power factor, α 2 σ, is typically optimized as a function of carrier concentration (typically around carriers/cm 3 ), through doping, to give the largest ZT. High mobility carriers are most desirable in order to have the highest electrical conductivity. Semiconductors have been primarily the materials of choice for thermoelectric applications. The best thermoelectric materials have a value of ZT 1 in their temperature range of operation. This value has been a practical upper limit for more than 30 years, yet no theoretical or thermodynamic reason exists for why it cannot be larger. From Equation 3, the value of Z can be raised by decreasing λ L. It can also be raised by increasing α 2 σ. However, σ is related to the λ E through the Wiedemann-Franz Law, and the ratio is essentially constant at a given temperature. Some of the goals of current research efforts are to find new materials that either enhance the efficiency of thermoelectric devices (increase ZT) or have the capability of operating in new and broader temperature regimes, especially at lower temperatures, T < 200 K.

5 SKUTTERUDITES 93 Recently there has been substantial renewed research interest in the investigation of new and/or significantly more efficient thermoelectric materials for applications in solid-state refrigeration or power generation. Over the past 30 years, alloys based on the Bi 2 Te 3 and Si-Ge systems have been extensively studied and optimized for their use as thermoelectric materials to perform a variety of solid-state thermoelectric refrigeration and power generation applications (1 3). There appears little room for improvement from these materials. Thus entirely new classes of compounds need to be investigated if substantial material improvements are to be made in this field (4, 5). Some of the new materials currently under investigation include skutterudites (6 10), quantum well materials (11), superlattice structures (12), and low-dimensional and disordered systems (12, 13). The enhanced interest in new thermoelectric materials has been driven by the need for higher performance and extended temperature regimes for thermoelectric devices in many civilian and military applications. The focus of this paper is on the skutterudite material system, one of the classes of materials that has drawn the most attention for thermoelectric applications. We review their interesting properties and their potential for future utilization as a next generation thermoelectric material. The Skutterudite Material System The skutterudites derive their name from a naturally occurring mineral, skutterudite or CoAs 3, first found in Skutterud, Norway. The structure is cubic and contains 32 atoms per unit cubic cell. A schematic showing the basic structure of the skutterudite unit cell is shown in Figure 3. A more detailed description of the crystal structure is given in the next section. Binary skutterudite compounds similar to CoAs 3 have shown interesting electronic properties. The skutterudite material system possesses the basic conditions for high ZT values. As described by Slack (15), these include a large unit cell, heavy constituent atom masses, low electronegativity differences between the constituent atoms, and large carrier mobilities. In addition, skutterudites form covalent structures with low coordination numbers for the constituent atoms and thus can incorporate atoms in the relatively large voids formed. Therefore, compounds can be formed with atoms filling the voids of the skutterudite structure. As first predicted by Slack (7), placing atoms in the interstitial voids of this crystal system would substantially reduce λ by introducing phonon-scattering centers. Thus these atomic void-fillers would rattle about in their oversized cages, thereby providing an approach to drastically reduce λ in the high-λ binary compounds and thereby maximize ZT. Another advantage of this cubic material system is that single crystals are not necessary to investigate the electrical and thermal transport properties of the skutterudites, which makes their promise for thermoelectric applications more feasible, that is, if the appropriate materials parameters can be achieved.

6 94 NOLAS, MORELLI & TRITT Figure 3 Schematic illustrating the unit cell of the unfilled skutterudite crystal structure. The concept of a phonon-glass electron-single-crystal (PGEC), first introduced by Slack and given in detail in a review (15), is at the heart of the investigation into the skutterudite material system for thermoelectric applications. A PGEC material would possess electronic properties normally associated with a good semiconductor single crystal but have thermal properties akin to that of an amorphous material. The introduction of this concept to thermoelectrics is one of the most significant innovations in the last 30 years. Although α 2 σ is relatively high for binary skutterudites, if this material system is to find use as a thermoelectric material, λ L must be reduced toward that of the theoretical minimum, λ min (7). Cahill et al (16) have enumerated a number of crystalline systems that possess low, glass-like λ L values. The relationship between glasslike λ L and λ min was pointed out by Slack (17). Of interest is the fact that the

7 SKUTTERUDITES 95 crystalline systems that possess glass-like thermal properties have features in common with the skutterudite system and thus investigating the possibility that the skutterudite material system may be synthesized to possess λ min values is highly relevant. STRUCTURE AND BONDING Crystal Structure The basic family of binary semiconducting compounds forming the skutterudite structure consists generally of CoP 3, CoAs 3, CoSb 3, RhP 3, RhAs 3, RhSb 3, IrP 3, IrAs 3 and IrSb 3. The skutterudite structure (indicated by MX 3 where M represents a metal atom and X a pnictide atom) belongs to the body-centeredcubic space group Im3 (18 21). The crystallographic unit cell consists of eight MX 3 units, with the eight M atoms occupying the c sites and the 24 X atoms situated on the g sites. The structure can be uniquely specified from the lattice constant and the two positional parameters y and z specifying the g site. The skutterudite structure can be considered a distortion of the more symmetric cubic perovskite ReO 3 structure (22). A key characteristic of the skutterudite structure is the nearly square four-membered rings of X atoms. These planar X 4 rings are mutually orthogonal and run parallel to the cubic crystallographic axes. The lattice constants, X-ray densities, and positional parameters for the known semiconductor binary skutterudite compounds are given in Table 1. From these data an estimate of the void radii of these compounds has been made (9). These are also listed in Table 1. In the skutterudite structure, each X atom has four nearest neighbors, two metal atoms and two nonmetal atoms situated at the corners of a distorted Table 1 Structural parameters of known binary skutterudites Lattice Void constant Density y z radius Compound (Å) (g cm 3 ) (Å) (Å) (Å) CoP CoAS CoSb RhP RhAs RhSb IrP IrAs IrSb

8 96 NOLAS, MORELLI & TRITT tetrahedron. Both the M-X bond distances and the X-X bond distances are short and nearly equal to the sum of the covalent radii, indicating strong covalent bonding. The M-M distances, on the other hand, are quite large, indicating that little bonding occurs between these atoms. Although the M-X bond distances are all equal, the X-X bond distances will be equal (and the nearly square planar rings, actually square planar) only if the positional parameters y and z satisfy the so-called Oftedal relation y + z = 0.5. As seen in Table 1, the Oftedal relation is not satisfied for any of these skutterudites. Furthermore, it has been shown (23) that to satisfy the Oftedal relation would require a much larger X-X distance and imply little X-X bonding. Thus the short X-X bond distances and the consequently strong X-X bonding are necessary for the stability of the skutterudite structure and have a large influence on the physical properties. Another prominent feature proven desirable for thermoelectric applications is the existence of two relatively large voids at the a positions of the unit cell that can be filled with additional atoms. The cubic unit cell can then be written in a general way as 2 M 8 X 24. Filled skutterudites have been formed, with lanthanide, actinide, and alkaline-earth ions interstitially occupying these voids (24). The interstitial ion in this structure is sixfold coordinated by the X-atom planar groups and is thereby enclosed in an irregular dodecahedral (12-fold) cage of X atoms. Figure 4 illustrates the unit cell of a filled skutterudite centered at the position of one of the interstitial guest ions. Large X-ray thermal parameters have been reported for these ions, indicating that these ions may rattle or participate in a soft phonon mode in the voids of this crystal structure (24 26). Indeed, the thermal parameters of these ions increase with decreasing ionic size. As first pointed out by Slack (7), the ions are caged in the voids of this structure and, if smaller than the void in which they are caged, may rattle and thus interact randomly with the lattice phonons, which results in substantial phonon scattering. This ball in a cage configuration of filled skutterudites is one of the most conspicuous aspects of the structure and directly determines some of the most important physical properties, as noted below. These compounds display an exceedingly rich spectrum of physical behavior, including semiconducting behavior, superconductivity, heavy fermion-like characteristics, and low-thermal conductivity all of which are a direct result of the nature of the structure and bonding in these materials. The above studies seem to imply that filling the skutterudite structure with electropositive ions in the voids necessitates the replacement of one of the constituent elements with another, electron-deficient neighbor in order to maintain structural stability. In fact, by alloying with Fe on the Co site or Sn on the pnictide site, compounds with lanthanide-filling fractions between zero and one have been obtained (27, 28). However, it is also possible to fractionally fill the binary skutterudites without any metal atom substitution. Thus La 0.2 Co 4 P 12

9 SKUTTERUDITES 97 Figure 4 The skutterudite unit cell centered at the lanthanide atom, which is enclosed in an irregular dodecahedral (12-fold) cage of X atoms ( filled circles). and Ce 0.25 Co 4 P 12 have been formed (29), as well as Ce 0.1 Co 4 Sb 12 (30) and La 0.23 Co 4 Sb 12 (28). The relationship between the metal atom charge state, the lanthanide valence, and structural and electronic stability of these compounds is subtle and important, and is discussed further below. Recently a novel approach to skutterudite compound synthesis has resulted in the preparation of many compounds that could not have been successfully formed employing traditional synthesis techniques. The formation of metastable skutterudite compounds in thin-film form was achieved through controlled crystallization of amorphous reaction intermediates formed by low-temperature interdiffusion of modulated elemental reactants (31 33). In this approach the elements are deposited sequentially in layers thin enough that the layers

10 98 NOLAS, MORELLI & TRITT interdiffuse before nucleation occurs. The formation of the desired metastable compound, for example FeSb 3, is achieved at low-temperatures from the amorphous intermediates that have the same composition. In this way the formation of more thermodynamically stable compounds, such as FeSb 2, can be avoided. By employing this technique, in addition to the binary skutterudite FeSb 3, filled skutterudites with the general formula TFe 4 Sb 12 were formed, with T being all the lanthanide group elements as well as hafnium. This technique was also used in the synthesis of filled skutterudite with void fillers even smaller than the large mass lanthanides. These included Sn, Al, Ga, In, and Zn (33). The formation of these new skutterudite compounds illustrates the need for continuing research and demonstrates the wide range of possible compounds that have yet to be tested for optimal thermoelectric properties. Crystal Chemistry One of the first observations made on binary skutterudites was that they are diamagnetic semiconductors. Given the above structural information, most authors (10, 34, 35) have described the bonding arrangement, with minor deviations, as follows: each X atom, which possesses 5 valence electrons, bonds with its two nearest neighbors in the X 4 groups via σ bonds, thereby involving 2 of its valence electrons. The remaining valence electrons of the X atoms (3 per atom) participate in the two M-X bonds. Because each metal atom is octahedrally coordinated by X atoms, there are a total of (3/2) 6 = 9 X electrons available for bonding in each MX 6 octahedron. The M atoms, possessing a s 2 d 7 configuration, can provide an additional 9 electrons, so that there are a total of 18 electrons available for this M-X arrangement. These are assumed to form d 2 sp 3 hybrid bonds. The octahedral ligand field of the X atoms splits the degenerate d-level into three lower energy non-bonding orbitals and two higher energy orbitals that hybridize with the metal atom s and p states to form the dps orbital complex, which provides the M-X bonding (36). Of the 18 electrons available for bonding, 6 fill the nonbonding orbitals in a spin-paired arrangement, whereas the remaining 12 fill the hybridized dps complex. These compounds possess no unpaired spins and therefore should be diamagnetic semiconductors, as has been reported. In NiP 3 this is not the case and metallic conductivity and paramagnetism occur (34). As discussed above, in filled skutterudites electron-deficient elements can be substituted for the constituents under concomitant occupation of the void in the skutterudite structure by a lanthanide, actinide, or alkaline-earth atom. In the case of M atom substitution, which has been the most popular way to synthesize filled skutterudites, the implication is that the M atom can remain in the d 6 state, with the filling atom transferring enough, or nearly enough, electrons to saturate the hybridized bonds. For example, in LaFe 4 P 12 for iron in the low

11 SKUTTERUDITES 99 spin Fe 2+ (d 6 ) state, the formula can be written as La 3+ [Fe 4 P 12 ] 4. With the transfer of three electrons from La 3+, the polyanion is just one electron deficient, and thus LaFe 4 P 12 should be metallic. For CeFe 4 P 12, if it is assumed that the cerium ion is in the tetravalent state, Ce 4+, one has Ce 4+ [Fe 4 P 12 ] 4 such that the CeFe 4 P 12 polyanion is isoelectronic with CoP 3, and thus CeFe 4 P 12 should be semiconducting. In this simplified but pertinent analysis, the question of the Fe atom charge state and the lanthanide ion valence has important consequences in determining whether these filled skutterudites are metallic or semiconducting. We return to this question in more detail below when the electrical properties of filled skutterudites are discussed. Band Structure Although the above crystal chemistry arguments serve as a useful starting point for the discussion of these materials and provide much insight into their electronic nature, a more realistic physical picture may be obtained from band structure calculations. Four such calculations have been published on binary skutterudites. One (37) uses the tight-binding method and essentially confirms the general predictions of the two electron bond model described above. Later, employing the linear augmented plane wave (LAPW) method, a calculation of the band structures of IrSb 3, CoSb 3, and CoAs 3 was carried out (38). These calculations showed a well-defined indirect gap between the valence and conduction bands from P to Ɣ for all three compounds. The magnitudes of the gap were 0.71, 0.57, and 0.73 ev for IrSb 3, CoSb 3, and CoAs 3, respectively. For IrSb 3, a direct gap of 1.21 ev was reported. Both the valence and conduction bands were derived from hybridized combinations of metal d and pnictide p bands. In addition to these bands, there is a remarkable band, also of hybridized d-p character, that crosses the gap and touches the conduction band at the Ɣ point in IrSb 3 and CoAs 3 and nearly does so in CoSb 3. Thus these binary skutterudites are actually zero or very narrow-gap semiconductors. Although this gap-crossing band is only one of many in the conduction and valence band manifold, and because it touches the conduction band very near to the Fermi level, its presence and nature should be reflected in transport measurements. As a result of the linear dispersion reported by the authors, it was predicted that the Seebeck coefficient of p-type materials with hole concentration p should vary as p 1/3 rather than p 2/3 as for a normal parabolic band. Finally, it was concluded that the conduction band is very flat, implying a large electron effective mass and the potential for excellent thermoelectric properties for n-type materials. Band structure calculations on CoP 3 and NiP 3, using the tight-binding method (39) and the self-consistent muffin-tin orbitals method (40), essentially confirm the findings of Singh & Pickett. Namely, there is an indirect gap of 1.26 ev in

12 100 NOLAS, MORELLI & TRITT CoP 3 and again a gap-crossing band with linear dispersion. For NiP 3 the band in the pseudo-gap region penetrates the conduction band and gives rise to its metallic behavior. Electronic band structure calculations have also been carried out on filled skutterudites. The first of these was performed on LaFe 4 P 12 using the tightbinding approach (37) from which it was concluded that this compound was metallic with the highest occupied band having a predominantly phosphorus character. Band structure calculations were carried out on LaFe 4 P 12 using the LAPW method (41). It was concluded that two bands cut through the Fermi energy, one originating from predominantly phosphorus p-states and the other, lying lower in energy, originating from iron d-states. These interesting thermoelectric properties stimulated further band structure calculations on CeFe 4 P 12 and CeFe 4 Sb 12 (42). The authors conclude that both materials are small band gap semiconductors, with gaps of 0.34 and 0.10 ev, respectively. Given the crystal chemistry arguments presented above, this would seemingly imply a Ce valence of 4+. On the contrary, this study concluded that Ce is nearly trivalent in these compounds, and the band gaps are a result of a strong hybridization of the cerium 4f levels with Fe 3d and pnictide p states. Because the experiments suggest that CeFe 4 Sb 12 is a metal (8), the authors concluded that their calculation slightly overestimated the magnitude of the band gap. A second band structure calculation using the LAPW approach was performed on La-filled skutterudites (43). In this study it was shown that the band structure of LaFe 3 CoSb 12 displays an indirect gap of approximately 0.6 ev. Similar to the conclusions of Harima (41), the highest occupied state is derived from bands with mostly Sb p character, but there are Fe/Co derived d-bands, the tops of which are situated only about 100 mev below the top of the p-like states. These d-band states have a very low dispersion and thus high effective mass which, according to these authors, gives rise to the large observed Seebeck coefficients. ELECTRONIC TRANSPORT PROPERTIES Binary Skutterudites The electronic transport properties of binary skutterudites were first studied in detail by Dudkin and coworkers in the Soviet Union in the late 1950s and early 1960s and centered on the properties of CoSb 3. From the exponential dependence of the conductivity on temperature, an energy gap of 0.5 ev was determined (44). This turns out to be quite close to the indirect gap estimated some forty years later by the band structure calculations described above (38). These same authors also explored the effect of Ni substitution on the electrical transport properties (45). They found that Ni could be substituted for Co up to

13 SKUTTERUDITES 101 a level of about 10% and that Ni acts as a donor. For low Ni concentrations (on the order of 1%), an increase in electron mobility was reported, whereas at higher concentrations, the mobility was reduced with respect to CoSb 3. Large values of α were observed consistent with the semiconducting nature of the compounds. This group then undertook a more thorough doping study of CoSb 3 (46) in which the influence of 13 different impurity elements on the thermoelectric and electrical transport properties was studied. Of these, four (Fe and Ni substituted for Co, and Sn and Te substituted for Sb) were found to be active dopants, with Ni and Te acting as donors and Sn as an acceptor. These authors describe the influence of Fe as a more subtle one: It is claimed that the Fe atoms do not determine directly the number and sign of the carriers, but rather drive the stoichiometry in the direction of increased antimony content. This increased Sb content is equivalent to the existence of vacancies on the Co sublattice and the appearance of hole conductivity. A further investigation of the normal dopants Sn, Te, and Ni was subsequently carried out (47). It was reported that while Sn-doped p-type samples exhibited rather high mobilities ( 10 3 cm 2 V 1 s 1 ), the mobilities in Te- and Ni-doped n-type material were much less ( 10 cm 2 V 1 s 1 ), which the authors attributed roughly to a factor of ten difference between hole and electron effective mass. Again, this result was essentially confirmed theoretically by the much later band structure calculations (38). The solubilities of Sn and Te in CoSb 3 were reported to be quite small ( 0.15 and 0.25%, respectively). Pleass & Heyding (48) studied the electrical properties of binary and ternary arsenides and concluded that CoAs 3, RhAs 3, and IrAs 3 are diamagnetic semiconductors and that both Ni and Fe in CoAs 3 are donor impurities. The (Fe,Ni)As 3 system, on the other hand, is quite different from the (Fe,Co)As 3 system, with the Ni and Fe appearing to form pairs and acting much like Co. The results on the binary and non-fe-containing ternary compounds are in accord with the one-electron bonding model, whereas the agreement for the Fe-containing compounds is not as satisfactory. Single crystals of the binary cobalt phosphides, arsenides, and antimonides were studied by Ackermann & Wold (49). These authors found that CoP 3 was a semiconductor with an optical band gap of 0.45 ev, whereas no such absorption edge was observed for either CoAs 3 or CoSb 3 ; the latter two compounds also exhibited a metallic resistivity. They concluded the σ bonding and σ antibonding bands are formed by anion bonding overlap in the arsenide and antimonide but are narrowed in the phosphide and thus form a gap. From optical and electrical measurements performed by Kliche & Bauhofer on a hot-pressed sample of RhSb 3 (50), it was concluded that this compound exhibited an extrinsic metallic behavior, while similar measurements by the same authors on CoAs 3 clearly exhibited a semiconducting character (51).

14 102 NOLAS, MORELLI & TRITT The electronic properties of binary skutterudites began to receive closer scrutiny when it was shown that these compounds can support high hole mobility. Caillat et al (52) fabricated single crystals of RhSb 3 with hole mobility as high as 10 4 cm 2 V 1 s 1 and CoSb 3 with mobilities approaching cm 2 V 1 s 1. All compounds were shown to possess large Seebeck coefficients consistent with a semiconducting behavior. Sharp et al (53) studied Co 1 x Ir x Sb 3 y As y alloys doped n-type with Ni, Te, or Pd and p-type with Fe, Ru, Os, and Ge. Samples doped n-type exhibited negative Seebeck coefficient at low temperature, which crossed over to positive values above 500 K, indicating the onset of intrinsic conduction and the predominance of the higher mobility holes over the electrons. In a low-temperature study of single crystals of CoSb 3 grown by the gradient freeze technique, Morelli et al (54) found that for samples doped p-type in the range of to cm 3, the mobility ranged from about 1800 to 2800 cm 2 V 1 s 1 at room temperature and approached 10 4 cm 2 V 1 s 1 at helium temperatures. It was concluded that the holes were scattered predominantly by phonons at high temperature and by neutral impurities at low temperature. They observed a metallic resistivity dependence attributed to a combination of a roughly constant hole concentration and the strongly increasing mobility. In addition, they found a peak in the Seebeck coefficient near 20 K that they attributed to phonon drag (see Figure 5). A similar peak in the low- temperature thermopower of IrSb 3 was found by Tritt et al (10) and also attributed to phonon drag. A very lightly doped single crystal of CoSb 3 grown using an Sb flux studied by Mandrus et al (55) exhibited a resistivity that decreased with increasing temperature, which the authors took as evidence of a 50 mev gap. At high temperatures, a second characteristic energy of 0.31 ev was observed in the resistivity. The authors suggested that this was consistent with the band structure calculations of Singh & Pickett (38). It was concluded that the low-temperature behavior of the mobility and Seebeck coefficient arose from the predominance of ionized impurity scattering. Anno et al (56) recently showed that the two types of behavior observed by Morelli et al (54) (metallic resistivity, high mobility, and neutral impurity scattering at low temperature) and Mandrus et al (55) (semiconducting resistivity, low mobility, and ionized impurity scattering at low temperature) could be reproduced by altering the grain size of hot pressed samples. For samples with 300 µm grains the metallic, neutral impurity behavior was observed, whereas for a sample with a 3 micron grain size the semiconducting, ionized impurity behavior was recovered. They attributed the difference to a change in predominant carrier-scattering mechanism with grain size. Arushanov et al (57) recently studied the electronic transport properties of lightly doped (down to cm 3 ) single crystals of CoSb 3. One sample had

15 SKUTTERUDITES 103 Figure 5 Seebeck coefficient of three p-type samples of CoSb 3 with different hole concentrations (after Reference 54). a room-temperature mobility of nearly 6000 cm 2 V 1 s 1. Like the sample of Mandrus et al (55), these samples exhibit a semiconductor-like resistivity and a mobility that falls off strongly at low temperature. Arushanov et al (57) attributed their results to the existence of an acceptor impurity band and an additional deep acceptor level. Caillat et al (58) studied the properties of CoSb 3 doped n-type with Ni and Te and p-type with Sn. From Hall and α measurements they estimated the hole and electron effective masses and their dependence on doping level. The

16 104 NOLAS, MORELLI & TRITT results confirmed the band structure calculations of a nonparabolic valence band and a heavy electron band. The dependence of carrier mobilities and Seebeck coefficients on carrier concentration is shown in Figure 6. The α data unfortunately do not span a large enough range in hole concentration to discern whether the results are described quantitatively by the band scheme of Singh & Pickett (38). Ternary Filled Skutterudites From the simple crystal chemistry arguments given above, it was expected that filling the Fe 4 X 12 network with a trivalent lanthanide ion would lead to an electron deficiency and thus metallic conductivity, whereas filling with a tetravalent rare earth or actinide element would fully saturate the polyanion and the compound would be semiconducting. It has since been shown that, indeed, most of the rare earth- and actinide-filled skutterudites are metallic with the exceptions of CeFe 4 P 12, UFe 4 P 12 (59), and possibly CeFe 4 As 12 (60). While the semiconducting behavior of CeFe 4 P 12 would be consistent with a tetravalent Ce state, it is more likely that the Ce is trivalent or perhaps at best intermediate valent. A gap, therefore, opens up at the Fermi level through strong hybridization between the rare earth 4f-states and conduction electrons; a similar effect would explain the semiconducting nature of the U-filled compound as well (59). Because of the very desirable heat conduction properties of filled-skutterudite antimonides for thermoelectric applications, there was strong motivation to attempt to return the electronic state to a semiconductor by use of counterdoping. Thus Chen et al (61) partially replaced Fe with Co and did observe a return to a semiconductor-like resistivity and an increase in Seebeck coefficient. It was noted by Morelli et al (30) that the replacement of Fe by Co in CeFe 4 Sb 12 causes a reduction in the amount of Ce filling the voids and that Fe/Co alloying and Ce filling are interrelated. They were able to achieve n-type doping at low Fe concentrations and showed that a small amount (10%) of Ce could be placed in the voids of CoSb 3 while acting as an n-type dopant. It should be noted that even filled skutterudites possessing metallic resistivity and large (10 21 cm 3 ) hole density tend to have large α, implying hole effective masses on the order of the free electron mass; n-type filled skutterudites have effective electron masses of several free electron masses. Thus as thermoelectric materials these compounds are extraordinary in that they achieve optimum properties in a carrier concentration range much more reminiscent of a metal or a semimetal than a moderately doped semiconductor. This remarkable behavior has its origin in the flat bands that arise from the hybridization of the rare earth 4f and metal d states. Along with their somewhat unusual electronic properties, it should be noted that several of the filled skutterudites are superconducting. Superconductivity in these compounds was first reported in LaFe 4 P 12 by Meisner (62). At the

17 SKUTTERUDITES 105 Figure 6 Dependence of (a) carrier mobility and (b) Seebeck coefficient on hole and electron concentrations for doped CoSb 3 (after Reference 54).

18 106 NOLAS, MORELLI & TRITT time, this was only the second known Fe-containing superconductor and the T c = 4.08 K is remarkably high for the high Fe concentration in this material. The existence of superconductivity in this material would imply that the Fe is nonmagnetic, and indeed subsequent Mössbauer measurements (63) showed that the Fe atom carries no moment in LaFe 4 P 12. Meisner also reported superconductivity near 7 K for LaRu 4 P 12 and near 1.8 K for LaOs 4 P 12. Recently, Shirotani et al (64) reported superconductivity at 10.3, 2.8, and 2.4 K, respectively, for LaRu 4 As 12, LaRu 4 Sb 12, and PrRu 4 As 12. THERMAL CONDUCTIVITY Introduction Although it had been known for some time (46) that CoSb 3 has a relatively large κ, partly due to its highly covalent cubic crystal structure, the investigation into the thermal properties of compounds with the skutterudite crystal structure was begun almost entirely with the proposition that this material system has potential for thermoelectric applications. Due to the importance of λ on ZT, an understanding of the mechanisms that may be employed for reducing λ in skutterudite compounds is imperative. In the list that follows, we have compiled the known methods for scattering phonons in skutterudite systems: point defect scattering, charge carriers from dopants, void fillers, inner-shell excitations, mixed valency, and structural defects (i.e. grain boundary, precipitates, and dislocations). In general, each one of these methods will scatter phonons in a particular frequency range while interacting weakly with all other frequency phonons. The combination of certain (or all) of these phonon scatterers will result in the largest reduction in λ, compared with that in binary skutterudites. Many of these phonon-scattering mechanisms have been well studied in semiconductor compounds. From this list we discuss those mechanisms that are most relevant to compounds with the skutterudite crystal structure. Binary (Unfilled) Skutterudites Figure 7 shows λ for three single-crystal CoSb 3 samples, along with calculated values using the Debye model (54). It is clear that these compounds display a typical crystalline temperature dependence similar in magnitude to that of InSb. The very steep rise in λ with decreasing temperature is characteristic of the predominance of phonon-phonon Umklapp scattering. The difference in the peak amplitude between these samples may be due to vacancies in the pnictide site, although this is not entirely clear. The compound IrSb 3 and the alloy Ir 0.5 Rh 0.5 Sb 3 also display a typical crystalline temperature dependence with λ L = 16 W/mK for IrSb 3 at room temperature and λ L = 9.1 W/mK for Ir 0.5 Rh 0.5 Sb 3 (7). These values are much higher than that calculated for the minimum thermal conductivity, λ min, of IrSb 3. This

19 SKUTTERUDITES 107 Figure 7 Thermal conductivity versus temperature for three CoSb 3 p-type crystals. The solid lines represent fits to the data assuming Umklapp and boundary scattering (upper curve) and including vacancies (lower curve) (after Reference 54). led the authors to postulate that filled skutterudites result in a large reduction in λ L owing to strong scattering from the rattling of the void-filling atoms in their oversized local sites in the crystal structure (7). Filled Skutterudites The major effort in the investigation of the skutterudite crystal system, particularly for thermoelectric applications, centers on the fact that atoms placed in the voids of this structure have a large effect on phonon propagation. This is most apparent from Figure 8, where λ L versus temperature is plotted for three lanthanide-filled polycrystalline skutterudites (9). Also shown in the figure

20 108 NOLAS, MORELLI & TRITT Figure 8 Lattice thermal conductivity (K L ) versus temperature of three filled skutterudites, IrSb 3, and the calculated K min for IrSb 3 (dashed line) (after Reference 9). is λ min of IrSb 3, which was calculated employing the formalism outlined in Slack (17), however, following Cahill et al (16) in taking the minimum mean free path of the acoustic phonons as one half the phonon wavelength. Also seen in Figure 8 is an order-of-magnitude decrease in λ L at room temperature, compared with that of IrSb 3, and an even larger decrease at lower temperatures. In addition, the smaller more massive lanthanide ion results in the lowest λ L. These smaller ions rattle more freely inside the voids of the skutterudite structure than does in La 3+ and are thereby able to interact with lower-frequency phonons than in the case of the La 3+ ions. In addition, the smaller lanthanide ions may also introduce a static disorder in the lattice at lower temperatures because they are more off-center than the larger ions. This guest ion-phonon coupling is an effective phonon-scattering mechanism and one that illustrates

21 SKUTTERUDITES 109 the potential of these materials for thermoelectric applications. In addition, the low-lying 4f electronic levels in the case of Nd 3+ and Sm 3+ also produce additional phonon scattering, further reducing λ L (9). This effect is most prominent in Nd-filled skutterudite of the three samples shown in Figure 8 due to the low lying ground-state energy levels of Nd 3+. Although the f-shell transitions are relatively weak phonon scatterers, compared with the disorder introduced by the lanthanide ion in the void of this structure, the effect is quite clear, particularly at lower temperatures (Figure 8). Figure 9 shows λ L for the Nd-filled skutterudite sample, as well as IrSb 3, expanded to low temperatures. The calculated λ min and λ for vitreous silica Figure 9 Lattice thermal conductivity (K L ) for the Nd-filled skutterudite sample expanded to low temperatures along with IrSb 3, vitreous silica (solid line), K min calculated for IrSb 3 (dashed line), and a calculation of grain boundary scattering for a 7-micron grain size sample (dotted-dashed line), the measured average grain size for the Nd-filled sample (after Reference 9).

22 110 NOLAS, MORELLI & TRITT are also shown in the figure. The Nd-filled skutterudite shows a temperature dependence that is atypical of crystalline solids, displaying no peak at low temperatures. The magnitude of λ L is lower than that of vitreous silica, with the exception of the plateau region that is typical of amorphous materials. This sample has the lowest λ L of any filled skutterudite reported due to the disorder created by the relatively small Nd 3+ ion in the large IrSb 3 cage, the inner shell 4f electronic excitation of Nd 3+, and the Ge-Sb point-defect scattering (9). For reasons that have been discussed above, much of the work on filled skutterudites has been devoted to the RFe 4 x Co x Sb 12 series of compounds, where R represents a lanthanide ion (6, 61). Figure 10 shows λ L versus temperature for polycrystalline CoSb 3, CeFe 3 CoSb 12, and LaFe 3 CoSb 12 (6). The λ e component of these filled skutterudites was rather large, approximately 40% of λ, confirming that these compounds are very heavily doped. Partial Void-Filling A small concentration of La or Ce in the voids of CoSb 3 results in a relatively large reduction in λ L (27, 28). This can be easily seen from Figure 11a, which shows Ce x CoSb 3 with the nominal concentration x = 0 and 0.1. The addition of Ce dramatically reduces λ L relative to CoSb 3. The weak temperature dependence is characteristic of the scattering due to the disorder induced by the Figure 10 Thermal conductivity versus temperature for polycrystalline CoSb 3, CeFe 3 CoSb 12, and LaFe 3 CoSb 12 (after Reference 6).

23 SKUTTERUDITES 111 Figure 11 Thermal conductivity versus temperature for (a) Ce y Co 4 Sb 12 for various Ce concentrations, y, along with typical results for crystalline CoSb 3 (solid line), and (b) Ce y Fe 4 x CoSb 12 for various Ce and Fe amounts, y and x, respectively (27, 28).

24 112 NOLAS, MORELLI & TRITT Ce 3+ ion. Very little Ce 3+ is required in order to produce a strong scattering effect. In Figure 11b, λ L as a function of temperature is shown for samples with nominal composition Ce y Fe 4 x Co x Sb 12 with varying y and x concentrations (Ce and Fe concentrations, respectively) (27). Again, very little Ce in the voids is required in order to produce a substantial phonon scattering effect. In addition, comparing the parts of Figure 11a with 11b we note that an additional reduction in λ L is observed in the Fe-containing samples compared with the non-iron-containing ones. As the Ce concentration is increased, the low-temperature peak is depressed and eventually vanishes, whereas at room temperature, λ L is relatively independent of Ce concentration but more dependent on the iron concentration. Because Fe and Co are nearly identical in mass and size, there seems to be an additional phonon-scattering mechanism(s) due to the iron substitution for Co in these compounds. This additional mechanism(s) is not known; however, only 3% of iron substituted for cobalt in CoSb 3 results in a relatively large reduction in λ L compared with CoSb 3, whereas 10% Fe in CoSb 3 results in a 50% reduction in λ L (28, 46). This effect may be related to the fact that Fe-containing skutterudites have a very low electronic mobility (see above). The effect of Fe in skutterudites requires further experimental, as well as theoretical, investigation in order to more fully understand this phenomenon. A further investigation into λ of Ce-filled Fe-containing compounds was accomplished in a series of compounds with different cerium-filling concentrations in conjunction with different Fe alloying in the Co site (27). The conclusion drawn from these results was that these compounds can be considered solid solutions of fully filled and unfilled skutterudites, i.e. solid solutions of CeFe 4 Sb 12 and 2 Co 4 Sb 12. Thus in addition to the disorder produced by the Ce 3+ ion in the oversized cage, there appears to be an additional mass fluctuation scattering between Ce 3+ and, the void in the crystal structure, which results in the observed reduction in λ L. In another report, La was used as void-filler (28). In that work λ L was measured up to a La concentration of 23%, the maximum solubility in CoSb 3. Further addition of La was accomplished by substituting Sn in the pnictide site. This approach was intended to eliminate the phonon-scattering mechanisms associated with magnetic scattering, as well as that due to Fe, leaving only the disorder introduced by the La 3+ ion in the oversized skutterudite voids. The conclusions from these results show that the greatest reduction of λ L occurs for samples with partial filling, as opposed to more fully filled, or of course unfilled, skutterudites. Employing the formalism of Callaway (65) and Abeles (66) it was shown that the random occupation of the void sites produces additional scattering that cannot be explained by that of mass-fluctuation scattering between empty void sites and La 3+ -filled ones. In addition, for small Ce 3+

25 SKUTTERUDITES 113 and La 3+ concentrations in CoSb 3, the thermal resistivity rises rapidly with lanthanide concentration, again much more so than can be predicted by a massfluctuation-type scattering mechanism. The main conclusion from the investigations into partially filled skutterudites was that these compounds demonstrate an interesting approach for further optimization of the transport properties for thermoelectric applications (27, 28). Valence Fluctuation An interesting phonon scattering mechanism observed in skutterudites is that attributed to multi-valency of a constituent forming the compound. The novel feature of this effect is that it appears to result from the charge transfer of a pair of electrons of opposite spin. This was discussed in detail in Nolas et al (67) where near-edge extended absorption fine structure analysis was used to determine the valence states of the constitutents in Ru 0.5 Pd 0.5 Sb 3. It was observed that ruthenium in this compound is in a 4+ and 2+ valence state, in approximately a 50:50 ratio. The model, which describes the low λ g measured in Ru 0.5 Pd 0.5 Sb 3 (λ L = 2.9 W/m K compared with 10.5 W/m K for CoSb 3 ), as well as that observed for other Ru-containing skutterudite compounds (68), is that of phonon scattering owing to the transfer of an electron pair in the d shell of Ru 2+ to a neighboring Ru 4+ (67). The scattering, therefore, depends on the presence of both charge states. This is different than scattering due to spin disorder observed in some transition-metal fluorides and oxides (67). SUMMARY AND CONCLUSIONS Many materials and synthesis techniques are being employed in the investigation of new and novel classes of materials for potential applications in solid-state thermoelectric applications. Slack has predicted that the quintessential material for these applications is what he describes as a phonon-glass-electron-crystal. In other words, the material has the thermal properties of a glass and the electrical transport properties of a crystalline material. In this review the authors hope they have conveyed the reasons for the intense research interest in the skutterudite crystal system and why these materials fulfill many of the qualities of the PGEC approach. The concept of introducing guest atoms into the voids of the open structure of these materials to essentially rattle around and effectively scatter phonons has resulted in greatly reducing the thermal conductivity of these compounds. This has resulted in relatively high ZT values in these skutterudite materials at elevated temperatures. Figure 12 shows a plot of ZT as a function of T from Sales et al (69), with the ZT approaching unity near 800 K. Fleurial et al (70) reported ZT 1.4 for Ce-filled skutterudites near